Elements of Geometry and Trigonometry |
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Page 11
... hypothenuse . Thus , in the triangle ABC , right - angled at A , the side BC is the hypothenuse . B 17. Among the quadrilaterals , we distinguish : The square , which has its sides equal , and its an- gles right - angles . The rectangle ...
... hypothenuse . Thus , in the triangle ABC , right - angled at A , the side BC is the hypothenuse . B 17. Among the quadrilaterals , we distinguish : The square , which has its sides equal , and its an- gles right - angles . The rectangle ...
Page 24
... hypothenuse and a side of the one , equal to the hypothenuse and a side of the other , each to each , the remaining parts will also be equal , each to each , and the triangles themselves will be equal . In the two right angled triangles ...
... hypothenuse and a side of the one , equal to the hypothenuse and a side of the other , each to each , the remaining parts will also be equal , each to each , and the triangles themselves will be equal . In the two right angled triangles ...
Page 47
... hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG , the half A of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop . XVII . ) ; hence , the two equal chords AB , DE ...
... hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG , the half A of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop . XVII . ) ; hence , the two equal chords AB , DE ...
Page 64
... hypothenuse CA common , and the side CB - CD ; hence they are equal ( Book I. Prop . XVII . ) ; hence AD is equal to AB , and also the angle CAD to CAB . And as there can be but one line bisecting the angle BAC , it follows , that the ...
... hypothenuse CA common , and the side CB - CD ; hence they are equal ( Book I. Prop . XVII . ) ; hence AD is equal to AB , and also the angle CAD to CAB . And as there can be but one line bisecting the angle BAC , it follows , that the ...
Page 78
... hypothenuse of a right angled tri- angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be right angled at A. Having described squares on the three sides , let fall from A , on the ...
... hypothenuse of a right angled tri- angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be right angled at A. Having described squares on the three sides , let fall from A , on the ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.